Geometry: Common Core (15th Edition)

by
Charles, Randall I.

Answer

x=30
y=90
angles measure 60, 120 and 60

Work Step by Step

Use the definition of a linear pair to write and solve equations.
Solve for y:
$(y+x)+(y-x)=180\longrightarrow$ a linear pair is supplementary
$2y=180\longrightarrow$ combine like terms
$y=90\longrightarrow$ division property of equality
Substitute and solve for x:
$2x+(y+x)=180\longrightarrow$ a linear pair is supplementary
$3x+y=180\longrightarrow$ combine like terms
$3x+90=180\longrightarrow$ substitute
$3x=90\longrightarrow$ subtraction property of equality
$x=30\longrightarrow$ division property of equality
Substitute to find the measure of each angle.
$2x=2(30)=60$
$y+x=90+30=120$
$y-x=90-30=60$